Nanostructures based on multiwalled carbon nanotubes (MWNTs) are fabricated using plasma of the mixture of hydrogen and nitrogen gases. The plasma-sharpened tips of nanotubes contain only a few tubes at the apex of the structure and lead to the dramatic enhancement in the emission current density by a factor >10(6) with the onset field as low as 0.16 V/mu m. We propose that the nature of the tunneling barrier changes significantly for a nanosize tip at very high local electric field and may lead to the saturation in the emission current density.